The 1-hole-missing and 7-hole-missing photonic crystal fibers (PCFs) with flattened fundamental modes (FMs) are proposed by introducing a layer of up-doped silica into the core of the PCFs. The transverse mode competitions are compared between the 7-hole-missing PCF lasers with and without flattened-FMs. The numerical results show that the flattened-FM PCF lasers can support the single transverse mode operation, even for a large value of the ratio of air hole diameter to the spacing between holes (up to 0.53).